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A local field is a topological field which is Hausdorff and locally compact as a topological space.
Examples of local fields include:
In fact, this list is complete--every local field is isomorphic as a topological field to one of the above fields.
This document is dedicated to those who made it all the way through Serre's book [1] before realizing that nowhere within the book is there a definition of the term “local field.”
- 1
- Jean-Pierre Serre, Local Fields, Springer-Verlag, 1979 (GTM 67).
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"local field" is owned by djao.
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(view preamble)
Cross-references: term, isomorphic, finite field, coefficients, variable, formal Laurent series, finite extension, complex numbers, real numbers, discrete topology, field, topological space, locally compact, Hausdorff, topological field
There are 8 references to this entry.
This is version 4 of local field, born on 2002-06-18, modified 2005-04-03.
Object id is 3119, canonical name is LocalField.
Accessed 3714 times total.
Classification:
| AMS MSC: | 11S99 (Number theory :: Algebraic number theory: local and $p$-adic fields :: Miscellaneous) | | | 12J99 (Field theory and polynomials :: Topological fields :: Miscellaneous) | | | 13H99 (Commutative rings and algebras :: Local rings and semilocal rings :: Miscellaneous) |
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Pending Errata and Addenda
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